Cohesive functions and weak accelerations. (English) Zbl 0808.30002

Ecalle, Jean

J. Anal. Math. 60, 71-97 (1993).

It is proved in this article that the class of cohesive functions exactly coincides with the class of weak accelerates, namely, of all functions obtainable by applying the so-called acceleration operators. The class of cohesive functions covers most quasianalytic Carleman classes, while removing their instability. In the first sections the author recalls the basic facts about Carleman quasianalyticity and Dyn’kin pseudoanalyticity; about cohesive functions and their stability; about the acceleration-deceleration operators and their integral kernels.
The main application following from this remarkable coincidence is now an elementary method for cohesive and quasianalytic continuation. The property of being cohesive has other various applications. The article contains minor misprints.

Reviewer: A.A.Melentsov (Ekaterinburg)

MSC:

30B40	Analytic continuation of functions of one complex variable
30D60	Quasi-analytic and other classes of functions of one complex variable

Keywords:

quasianalytic Carleman classes; quasianalytic continuation

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